A new ordering for stochastic majorization: theory and applications

Cheng‐Shang Chang

50 citations0/0 files storedAdvances in Applied Probability

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Advanced Queuing Theory Analysis Probability and Statistical Research Mathematical Inequalities and Applications

Abstract

In this paper, we develop a unified approach for stochastic load balancing on various multiserver systems. We expand the four partial orderings defined in Marshall and Olkin, by defining a new ordering based on the set of functions that are symmetric, L-subadditive and convex in each variable. This new partial ordering is shown to be equivalent to the previous four orderings for comparing deterministic vectors but differs for random vectors. Sample-path criteria and a probability enumeration method for the new stochastic ordering are established and the ordering is applied to various fork-join queues, routing and scheduling problems. Our results generalize previous work and can be extended to multivariate stochastic majorization which includes tandem queues and queues with finite buffers.

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1986Comparison Methods for Queues and Other Stochastic Models.1984Comparison Methods for Queues and Other Stochastic Models 1977Optimality of the shortest line discipline 1978On the optimal assignment of customers to parallel servers 1988Approximate analysis of fork/join synchronization in parallel queues 1980A simple dynamic routing problem 1986Deciding Which Queue to Join: Some Counterexamples 1986Deciding which queue to join: Some counterexamples

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1995Sample path methods in the control of queues 1999Structural Analysis of a Queueing System with Multiclasses of Correlated Arrivals and Blocking 1993On the duality between routing and scheduling systems with finite buffer space 1994Analysis of a Customer Assignment Model with No State Information 1994Sample Path Criteria for Weak Majorization

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